Leonhard Euler

(1707 – 1783)

Leonhard Euler was an astonishingly gifted and prolific mathematician. Born in Basel, Switzerland in 1707, Euler is considered the greatest mathematician and theoretical physicist of the eighteenth century, and a leading mathematical universalist. There is virtually no branch of mathematics unaffected by his genius; in more than 900 books and papers, Euler conveyed his discoveries in geometry, calculus, probability, number theory, and algebra. His work in applied mathematics generated important contributions to optics, mechanics, navigation, astronomy, acoustics, statistics, and finance. These achievements are even more remarkable considering that, for much of his life, Euler was blind.

No other mathematician has had more influence than Euler on modern notation. He introduced the use of f(x) to indicate a function of x; a, b, and c and A, B, and C to designate, respectively, the sides and angles of a triangle; π to express the ratio of the circumference of a circle to its diameter; i to symbolize the square root of -1; and e to denote the base of natural logarithms.

Euler was profoundly influenced by his father, Paul, who had studied under the noted Swiss mathematician Jakob Bernoulli. Leonhard knew while he was still very young that he wanted to be a mathematician, but his father, a Calvinist priest, had planned for Leonhard to succeed him as pastor of his parish. Leonhard dutifully studied theology at the University of Basel and at the age of sixteen was awarded a master’s degree; however, at the same time, he was tutored in mathematics by Johann Bernoulli, the brother of his father’s teacher. Fortunately, Bernoulli was able to convince the elder Euler of Leonhard’s mathematical genius. Paul Euler reluctantly abandoned his ambitions for his son, and was thereafter supportive of Leonhard’s decision to pursue a career in mathematics. Leonhard, in turn, was a fervent Calvinist all his life.

Leonhard Euler’s friendship with Johann Bernoulli’s sons, Nikolaus and Daniel, was instrumental in shaping Euler’s career. He had applied at the age of nineteen for a post at the University of Basel but was rejected, probably because of his youth. When the Bernoullis learned that Euler was seeking employment, they obtained a position for him at the newly established St. Petersburg Academy of Sciences in Russia, where they were professors of mathematics. Euler left for Russia in 1727, and never returned to the land of his birth.

Teaching was of secondary importance at the St. Petersburg Academy. Like others of its time, the Academy was founded primarily to facilitate scientific research and publish the findings of its faculty. Euler was an unqualified success; within three months of his arrival, he had written the first of hundreds of books and papers elucidating his discoveries.

His extravagant effort was not without cost. Euler had amazed scientists at the Academy by solving, within three days, a complex problem in astronomy; they had expected him to be working on the question for months. Shortly thereafter, Euler contracted a serious illness attributed to overwork. The accompanying fever destroyed the vision of his right eye, but not his extraordinary productivity.

Euler’s brilliant discoveries were widely disseminated, earning him the respect of scientists and mathematicians throughout Europe. In 1728, when Euler was just twenty-one years old, Johann Bernoulli, Euler’s former tutor, deemed him to be the “most learned and gifted man of science.” Bernoulli’s opinion was shared by many.

Despite the accolade that followed him throughout his life, Euler was a humble man. When asked by an admirer how he was able to work so quickly and yet so accurately, Euler blushingly responded, “My pencil is more intelligent than I am.” He carefully recorded his failures, thus steering others from fruitless paths. As one of his biographers has noted, “Even when he stumbled, Leonhard Euler left behind signs of great insight. Such, perhaps, is the mark of genius.”

In 1733, Euler married Katharina Gsell, the daughter of a Swiss artist living in St. Petersburg. Johann, the first of their thirteen children (eight of whom died in childhood), was born in 1734. Johann would later become his father’s collaborator, and in 1769 was appointed the Academy’s permanent secretary.

Leonhard Euler was intrigued by a problem posed in 1735 by the residents of Königsberg, Germany. Built on an island in the Pregel River, Königsberg was connected by seven bridges to the mainland and an adjacent island. Could each bridge be crossed once, and only once? In proving mathematically the impossibility of such a route, Euler invented Analysis Situs, or topology, a branch of geometry.

Russia’s political atmosphere, replete with executions and sedition, had grown so unstable by 1741 that Euler eagerly accepted King Frederick’s offer of a post at the Berlin Academy. For twenty-five years, Euler was Germany’s premier mathematician. Though this period was Euler’s most productive, it was not his most pleasant. The irreverent Frederick scorned Euler’s piety, and saw little purpose in higher mathematics. He sharply criticized Euler’s management of the Academy and its financial affairs, and made crude jokes at Euler’s expense. In 1765, Euler implored the king to accept his resignation. Frederick, recognizing the prestige afforded his court by a man of Euler’s caliber, refused to allow him to leave Germany.

Frederick would have prevailed had Euler not had a powerful ally in Catherine the Great, who had seized power in Russia in 1762. A leading proponent of the European Enlightenment, Catherine was determined to revivify the St. Petersburg Academy; a first step toward that end was retrieving Euler. Catherine added the weight of her considerable influence to Euler’s plea for release from Germany. By June 1766, Frederick had capitulated, and Euler and his family were on their way to Russia.

Euler was warmly welcomed in St. Petersburg, and lavishly supported by the Russian throne. Shortly after his return, however, he developed cataracts that destroyed what vision remained to him. Undaunted, he dictated his calculations to his sons and students. Euler’s phenomenal powers of memory and concentration enabled him to visualize formulae that, when written, filled several pages.

Euler’s productivity continued until September 18, 1783, the day of his death. He accurately calculated the orbit of the newly-discovered planet, Uranus, hours before being struck by a fatal cerebral hemorrhage. Euler was buried in St. Petersburg’s Lutheran Smolenskoye Cemetery, where a massive monument was later erected in his honor.

Links

http://www-history.mcs.st-andrews.ac.uk/Biographies/Euler.html

References

• Asimov, Isaac. Asimov’s Biographical Encyclopedia of Science and Technology. Garden City, New York: Doubleday & Company, Inc., 1972.
• Burckhardt, J. J. “Leonhard Euler, 1707–1783.” Mathematics Magazine 56 (November 1983): 262–273.
• Dunham,William. “Euler and the Fundamental Theorem of Algebra.” The College Mathematics Journal 22 (September 1991): 282–293.
• Gillispie, Charles Coulston, ed. Dictionary of Scientific Biography. Vol. IV. New York: Charles Scribner’s Sons, 1971.
• Hooper, Alfred. Makers of Mathematics. New York: Random House, Inc., 1948.
• Kasner, Edward and James Newman. Mathematics and the Imagination. New York: Simon and Schuster, 1963.
• Weil, André. “Euler.” The American Mathematical Monthly 91 (November 1984): 537–542.